I have been proofreading stuff for as long as I can remember. I write English papers that get 98s and 99s-from a teacher who doesn't give 100s on principle. I proofread the program for my mother's theatre troupe, and I'm a paid copyeditor and theatre reporter for my school, or I was until the paper collapsed.
I automatically proofread as I read-if you've gotten a review from me before, look at it. If I say I loved it, there's probably little I would change if you sent it to me to beta. If I give you constructive criticism, that's what you'd get from me as a beta, only more in depth, generally with specific examples and ideas on how to fix them. If I didn't comment, it probably just didn't work for me-see weaknesses. Unless I favorited it, and then I probably loved it and just didn't have anything else to say, nothing specific that stood out.
If you want a litmus test on whether I'll be a useful beta, send me a PM and ask me to review something you've got, unbeta'd, obviously. If you beta all your stories before posting, send me a PM and ask me for a connection, then send me the file and ask me for a review. I won't agree to beta something that I can't see a sample of.
I ask that you have a plan for a story. I don't require an outline, but I don't like stories where the author gives his or her characters new problems, gets them out again, gets them into new problems, and then puts "I'm running out of ideas, guys," in the A/N and abandons the story-because that author never had a plan, just a desire to write fanfiction and ideas for a few scenes. You should know how it ends, or at least plan to end it at a certain point. Example: You're writing a Sherlock fic that you know involves Sherlock faking his death and John coping while Sherlock goes off on a secret mission. You don't have to know the details of the mission or exactly what John's up to, but you better know that you're going to end it when Sherlock comes home to John. Or after Sherlock comes home to John and they get together, whatever you want. On this topic, I prefer to know what's coming. Yes, spoilers, but I'm your editor, not your audience, and I can't tell if you're leaving plot holes (or providing extraneous, distracting information) if I don't know what's important to the plot and what's not. Again, I don't need a chapter by chapter outline, just as much as you can give me.